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Consistency relations of large-scale structures provide exact nonperturbativeresults for cross-correlations of cosmic fields in the squeezed limit. Theyonly depend on the equivalence principle and the assumption of Gaussian initialconditions, and remain nonzero at equal times for cross-correlations of densityfields with velocity or momentum fields, or with the time derivative of densityfields. We show how to apply these relations to observational probes thatinvolve the integrated Sachs-Wolfe effect or the kinematic Sunyaev-Zeldovicheffect. In the squeezed limit, this allows us to express the three-pointcross-correlations, or bispectra, of two galaxy or matter density fields, orweak lensing convergence fields, with the secondary Cosmic Microwave Background(CMB) distortion in terms of products of a linear and a nonlinear powerspectrum. In particular, we find that cross-correlations with the integratedSachs-Wolfe effect show a specific angular dependence. These results could beused to test the equivalence principle and the primordial Gaussianity, or tocheck the modeling of large-scale structures.

Consistency relations for large-scale structures: Applications for the integrated Sachs-Wolfe effect and the kinematic Sunyaev-Zeldovich effect